Ketchup
Although most ketchup bottles will instruct you to refrigerate after opening, ketchup generally has enough preservatives to keep it from spoiling without refrigeration. Many restaurants will keep ketchup bottles on the table for extended periods of time.
Pickles
Most pickles are refrigerated, but really don’t need to be. The way most pickles are made, including the high salt content, makes it unnecessary to keep them at refrigerated temperatures. In fact, pickling is often used as a food preservation method.